A potential field is given by V = 3x^2y - yz. Which of the following is not true?
(a) At point (1, 0, -1) V and E vanish.
(b) x^2y = 1 is an equipotential line on the xy-plane.
(c) The equipotential surface V = - 8 passes through point P + 2, -1, 4)
(d) The electric field at P is 12ax - 8ay - az V/m.
(e) A unit normal to the equipotential surface V = - 8 at P is -0,83ax + 0,55ay+ 0,07az.
Gives
"V=3x^2y-yz"
"V_{(1,0,1)}=0"
"E=-\\nabla V"
"E=-4a_y"
Option (a) wrong(incorrect)
"P=x^2y-1"
Equpotential line equation
Equation (2) is lies xy-plane
Option (b) is correct option
Electric field
"V=3x^2y-yz"
Option (c) is correct
"E=12a_x-8a_y-a_z"
Option (d) correct
"E=12ax-8ay-az"
"\\hat{V}=\\frac{\\nabla V}{ |\\nabla V|}"
"\\hat{V}=\\frac{6axy a_x+(3x^2-z)a_y+a_z(-y)}{14.5}"
"\\hat{V}=-0.83a_x+0.55a_y+0.07a_z"
Option (e) is correct
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